Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
Department of Clinical and Biological Sciences, Università degli Studi di Torino, Regione Gonzole 10, 10043 Orbassano, Italy.
Philos Trans R Soc Lond B Biol Sci. 2020 Sep 14;375(1807):20190383. doi: 10.1098/rstb.2019.0383. Epub 2020 Jul 27.
Collective dynamics in animal groups is a challenging theme for the modelling community, being treated with a wide range of approaches. This topic is here tackled by a discrete model. Entering in more details, each agent, represented by a material point, is assumed to move following a first-order Newtonian law, which distinguishes speed and orientation. In particular, the latter results from the balance of a given set of behavioural stimuli, each of them defined by a direction and a weight, that quantifies its relative importance. A constraint on the sum of the weights then avoids implausible simultaneous maximization/minimization of all movement traits. Our framework is based on a minimal set of rules and parameters and is able to capture and classify a number of group dynamics emerging from different preferred behaviour, which possibly includes attractive, repulsive and alignment stimuli. In the case of a system of animals subjected only to the first two behavioural inputs, we also show how analytical arguments allow us to relate the equilibrium interparticle spacing to critical model coefficients. Our approach is then extended to account for the presence of predators with different hunting strategies, which impact on the behaviour of a prey population. Hints for model refinement and applications are finally given in the conclusive part of the article. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.
动物群体的集体动力学是建模界的一个具有挑战性的主题，人们采用了广泛的方法来处理这个问题。本主题通过一个离散模型来解决。更详细地说，每个代理（由一个物质点表示）被假设遵循一阶牛顿定律，该定律区分速度和方向。具体来说，后者是由一组给定的行为刺激的平衡产生的，每个刺激都由一个方向和一个权重来定义，权重量化了其相对重要性。然后，对权重总和的约束避免了所有运动特征同时不合理地最大化/最小化。我们的框架基于一组最小的规则和参数，可以捕捉和分类许多不同偏好行为产生的群体动力学，这些行为可能包括吸引力、排斥力和对齐刺激。在仅受到前两种行为输入的动物系统的情况下，我们还展示了如何通过分析论证将平衡粒子间间距与关键模型系数联系起来。然后，我们将方法扩展到考虑具有不同狩猎策略的捕食者的存在，这些策略会影响猎物种群的行为。最后，在文章的结论部分给出了模型改进和应用的提示。本文是主题为“生物系统中集体迁移的多尺度分析和建模”的一部分。
